def CarrBSCV(n, s0, K, T, model, a=100):
'''
input model must have vol() implemented
'''
s0, K, T, a = map(float, (s0, K, T, a))
k = math.log(K)
b = 1.5
r = model.r
c1, c2 = model.cumulants(1)[:2]
modelCV = BSCV(c1, c2)
modelCV.setIR(r)
'''
intgDiff = lambda u: ((cmath.exp(1j*(-u*k + (u-(b+1)*1j)*math.log(s0)))*math.exp(-r*T) \
*model.chf(u - (b+1)*1j, T) \
- cmath.exp(1j*(-u*k + (u-(b+1)*1j)*(math.log(s0) )))*math.exp(-r*T) \
*modelCV.chf(u - (b+1)*1j, T)) \
/(b**2 + b - u**2 + (2*b+1)*u*1j)).real
'''
intgDiff = lambda u: (
cmath.exp(1j * (-u * k +
(u -
(b + 1) * 1j) * math.log(s0))) * math.exp(-r * T) *
(model.chf(u - (b + 1) * 1j, T) - modelCV.chf(u - (b + 1) * 1j, T)) /
(b**2 + b - u**2 + (2 * b + 1) * u * 1j)).real
return math.exp(-b * k) * fnc.trap(
n, intgDiff, 0, a) / math.pi + modelCV.callforCarr(s0, K, T)
def Lewis(n, s0, K, T, model, a=100):
s0, K, T = map(float, [s0, K, T])
r = model.r
integrand = lambda u: (cmath.exp(u * (math.log(s0 / K)) *
(1j) - 0.5 * r * T) * model.chf(
u - 0.5j, T) / (u**2 + 0.25)).real
return s0 - math.sqrt(s0 * K) * math.exp(-0.5 * r * T) * fnc.trap(
n, integrand, 0, a) / math.pi
def Carr(n, s0, K, T, model, a=100):
s0, K, T, a = map(float, (s0, K, T, a))
k = math.log(K)
b = 1.5
r = model.r
integrand = lambda u: (cmath.exp(1j * (-u * k +
(u - (b + 1) * 1j) * math.log(s0)))
* math.exp(-r * T) * model.chf(u -
(b + 1) * 1j, T) /
(b**2 + b - u**2 + (2 * b + 1) * u * 1j)).real
return math.exp(-b * k) * fnc.trap(n, integrand, 0, a) / math.pi
def CarrRealBSCV(n, s0, K, T, model, a=100):
'''
input model must have vol() implemented
'''
s0, K, T, a = map(float, (s0, K, T, a))
k = math.log(K)
b = 1.5
r = model.r
modelCV = BS(model.vol())
modelCV.setIR(r)
intgDiff = lambda u: (
cmath.exp(1j * (-u * k +
(u -
(b + 1) * 1j) * math.log(s0))) * math.exp(-r * T) *
(model.chf(u - (b + 1) * 1j, T) - modelCV.chf(u - (b + 1) * 1j, T)) /
(b**2 + b - u**2 + (2 * b + 1) * u * 1j)).real
return math.exp(-b * k) * fnc.trap(n, intgDiff, 0,
a) / math.pi + modelCV.call(s0, K, T)